In section  \(\ref {sec:res}\) , we observed that the notion of partial invariance allowed us to explore the inherent trade-off between risk minimization and fairness and in certain cases, simultaneously improve upon both risk and fairness as compared to the IRM solution. However, it is not yet clear as to how partial invariance fits in the “causal” picture of invariant risk minimization. We attempt to shed some light on this by slightly modifying the motivating regression task in the original IRM formulation [1]}.
